Switch pydrake bindings from pybind11 to nanobind

[jwnimmer-tri]

Is your feature request related to a problem? Please describe.

Drake's pydrake bindings layer is a pain point in various ways:

• Must rebuild for every single python minor version we support.
• Slow compile times.

The former is annoying not only for build times, but also because it takes up way more space on PyPI per release, which leads to things like pypi/support#3226 where we burn through our quota 3-4x faster than we should be doing. Ideally, our bindings library should support Python's Stable API, also know as abi3.

Describe the solution you'd like

Port pydrake to use nanobind instead of pybind11.

Describe alternatives you've considered

There are various other pybind11-inspired bindings libraries, but none of them seem to support abi3.

Additional context

My current thinking is that the first step should be #19250, i.e., removing all of Drake's customization of pybind11. After that, we can follow https://nanobind.readthedocs.io/en/latest/porting.html to move from vanilla pybind11 to nanobind.